Nanomedicine, Volume I: Basic Capabilities

© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

 

4.6.1 Minimum Detectable Temperature Change

A sensor system consisting of N atoms has (3N-6) internal coordinates and thus ~(3N-6) oscillators, each with an average energy of ~kT assuming no modes are high enough to be frozen out. However, the standard deviation of the energy of the oscillators around the mean energy is ~kT, and these energy fluctuations are uncorrelated (ignoring coupling between the oscillators), so (3N-6) of them will have an average fluctuation of kT (3N-6)1/2. (By comparison, the energy in one 10-micron infrared photon is ~5 kT.) As a result, an instantaneous measurement of the total energy of all N atoms gives a minimum detectable temperature change DTmin of

{Eqn. 4.34}

for a set of Nmeas independent temperature measurements using a sensor of volume Vsensor constructed with material of atomic number density nd, which might be maximized using diamond (nd = 1.76 x 1029 carbon atoms/m3).

Thermal equilibration time tEQ ~ L2 CV / Kt (Eqn. 10.24) for a sensor of size L, of heat capacity CV (1.8 x 106 joules/m3-K for diamond) and of thermal conductivity Kt (2000 watts/m-K for diamond460). Thus, tEQ ~ 10-13 sec for a sensor of size L = 10 nm, 10-11 sec for L = 100 nm, and 10-9 sec for L = 1 micron, so thermal sensors up to 1 micron in size should easily achieve thermal equilibration within a typical measurement cycle time Dtmin ~ 10-9 sec. Sensor measurement time tmeas = Nmeas Dtmin.

A (57 nm)3 sensor can detect DTmin / T = 10-4 (~31 millikelvins at 310 K) in a single measurement (Nmeas = 1), with measurement time tmeas ~ 1 nanosec. A sensitivity of DTmin / T = 10-6 (~310 microkelvins at 310 K) may be achieved using either a ~1 micron3 sensor with a single measurement (Nmeas = 1, tmeas = 1 nanosec) or a (124 nm)3 sensor with Nmeas = 1000 independent measurement cycles and tmeas = 1 microsec. Finally, a 1 micron3 sensor can detect DTmin / T = 3 x 10-9 (~1 microkelvin at 310 K) with Nmeas = 100,000 independent sensor cycles, giving a measurement time tmeas ~ 100 microsec.

These figures are confirmed by experimental estimates of detector noise temperature, such as DTmin / T = (k / L3 CV)1/2 ~ 10-6 for a silicon nitride detector678 with CV = 5.2 x 106 joules/m3-K and L ~1 micron. It has been calculated that sensitivity of ~1 microkelvin is theoretically possible using quartz electronic microresonators as precision thermometers.462,1699 Thermocouple probes with 100 nm tips have already shown ~100 microkelvin sensitivity,463 tunneling thermometers capable of measuring thermoelectric potential localized to atomic-scale dimensions have been proposed,464 and experiments leading toward "yoctocalorimetry" were being pursued in 1998.2928

For comparison, heat sensors in human skin have DTmin / T ~ 3 x 10-4 (~90 millikelvins), and the infrared sensor pit of the rattlesnake is sensitive to an energy intensity of ~0.8 pJ/micron2 in a measurement time tmeas ~35 millisec and achieves DTmin / T ~ 3 x 10-6;701,826 mosquitos register DTmin / T ~ 6 x 10-6 at a distance of ~1 cm.

 

Last updated on 17 February 2003